
11-08-24 AP Calculus AB VL Ch 3 Review
Flashcard
•
Mathematics
•
12th Grade
•
Practice Problem
•
Hard
Standards-aligned
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15 questions
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1.
FLASHCARD QUESTION
Front
What is the relationship between the derivatives of inverse functions?
Back
If g(x) = f^{-1}(x), then g'(x) = 1 / f'(g(x)).
Tags
CCSS.HSF-BF.B.4A
2.
FLASHCARD QUESTION
Front
What is the Chain Rule in calculus?
Back
The Chain Rule states that if you have a composite function f(g(x)), then the derivative is f'(g(x)) * g'(x).
3.
FLASHCARD QUESTION
Front
How do you find dy/dx using implicit differentiation for the equation f(x)g(y) = C?
Back
Differentiate both sides with respect to x, applying the product rule and chain rule as necessary, and solve for dy/dx.
4.
FLASHCARD QUESTION
Front
What is the derivative of ln(x)?
Back
The derivative of ln(x) is 1/x.
5.
FLASHCARD QUESTION
Front
How do you differentiate a function of the form f(g(x))?
Back
Use the Chain Rule: f'(g(x)) * g'(x).
6.
FLASHCARD QUESTION
Front
What is the second derivative of a function?
Back
The second derivative is the derivative of the first derivative, denoted as f''(x).
7.
FLASHCARD QUESTION
Front
What is the fourth derivative of y = 2 ln(x)?
Back
The fourth derivative is -12/x^4.
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